The Mass of the White Dwarf in the Recurrent Nova U Scorpii

Mon. Not. R. Astron. Soc. 000, 000–000 (2001)

The mass of the white dwarf in the recurrent nova U Scorpii

T. D. Thoroughgood,1? V. S. Dhillon,1 S. P. Littlefair,1 T. R. Marsh,2 D. A. Smith1,3 1Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK 2Department of Physics and Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK 3Winchester College, Winchester SO23 9LX, UK

Accepted for publication in the Monthly Notices of the Royal Astronomical Society

17/07/2001

ABSTRACT We present spectroscopy of the eclipsing recurrent nova U Sco. The radial velocity semi- 1 amplitude of the primary star was found to be KW =93 10 km s− from the motion of the wings of the HeII λ4686A˚ emission line. By detecting± weak absorption features from the secondary star, we find its radial velocity semi-amplitude to be KR = 170 10 1 ± km s− . From these parameters, we obtain a mass of M1 =1.55 0.24M for the white ± dwarf primary star and a mass of M2 =0.88 0.17M for the secondary star. The ± radius of the secondary is calculated to be R2 =2.1 0.2R , confirming that it is ± evolved. The inclination of the system is calculated to be i =82.7◦ 2.9◦, consistent with the deep eclipse seen in the lightcurves. The helium emission± lines are double- peaked, with the blue-shifted regions of the disc being eclipsed prior to the red-shifted regions, clearly indicating the presence of an accretion disc. The high mass of the white dwarf is consistent with the thermonuclear runaway model of recurrent nova outbursts, and confirms that U Sco is the best Type Ia supernova progenitor currently known. We predict that U Sco is likely to explode within 700 000 years. ∼ Key words: accretion, accretion discs – binaries: eclipsing – binaries: spectroscopic – stars: individual: U Sco – novae, cataclysmic variables.

1INTRODUCTION runaway (TNR) model of classical novae outbursts (e.g. ?). In this model, the primary star builds up a layer of mate- U Sco belongs to a small class of cataclysmic variables (CVs) rial, accreted from the secondary star, on its surface. The known as recurrent novae (RNe), which show repeated nova temperature and density at the base of the layer become outbursts on timescales of decades. Of these, U Sco has the sufficiently high for nuclear reactions to begin. After igni- shortest recurrence period ( 8 y), with recorded outbursts tion, the temperature rises rapidly and the reaction rates in 1863, 1906, 1936, 1979, 1987∼ and 1999. It is likely that run away, until the radiation pressure becomes high enough others have been missed due to its proximity to the ecliptic to eject most of the accreted material. This process occurs (4◦). when the accreted layer reaches a critical mass (?), the value The RN class is further divided into three groups, de- of which is a strongly decreasing function of the white dwarf pending on the nature of the secondary star (red giant, sub- mass. Therefore, to reduce the time interval between erup- giant or dwarf), each of which have different eruption mech- tions to those observed in the RNe, either the mass accre- anisms (see ? & ? for reviews). U Sco is the only object of tion rate (M˙ ) or the white dwarf mass must be increased. the three in the sub-giant class which eclipses ( ), and also ? For RNe, the white dwarf mass is the more important con- shows evidence of secondary absorption lines (?), making it straint because there is an upper limit to M˙ above which the the best candidate for the determination of system parame- degeneracy on the surface of the white dwarf weakens, and ters. no powerful eruption can occur. For this model to account The outburst mechanism for the U Sco sub-class of RNe for the short times between outbursts as seen in RNe, the is believed to be a modified version of the thermonuclear white dwarf must have a mass close to the Chandrasekhar limit. A tight constraint on the white dwarf mass in U Sco

? E-mail: [email protected] 2 T. D. Thoroughgood et al. is hence theoretically important, as it will provide a direct observational test of the TNR model for this group of RNe. The mass of the white dwarf in U Sco is also important in terms of binary evolution and the role of RNe as Type Ia supernova progenitors. ? suggested, on the basis of the abundance determinations of the ejecta of RNe, that the mass of the envelope ejected during the outburst might be smaller than the amount of accreted material. In the case of high mass white dwarf systems, the primary could be pushed over the Chandrasekhar limit to produce a supernova explosion. A tight constraint on the white dwarf mass and the mass accretion rate allows the time to supernova to be calculated, which according to ?, could be as little as 50 000 years. There have been two previous attempts to measure the mass of the white dwarf in U Sco. ? attempted to use low Figure 1. R-band lightcurve of the 1999 outburst of U Sco. The resolution spectra to determine the radial velocity semi- data have been taken from ?. The open circle represents a mea- amplitude of both components by looking at the emission surement with an unrecorded error. and absorption line shifts. They calculated a white dwarf mass of 0.23–0.60M , a result disputed by ?,whoobtained

10 spectra with poor phase coverage, but were able to conclude a high primary mass, although their errors were large (M1 =1.16 0.69M ). ? re-phased the radial velocity mea- ± Table 1. Journal of observations for U Sco. Orbital phase is cal- surements of ? and ? using a new orbital period. They con- culated using the new ephemeris presented in this paper (equation cluded that due to inconsistent γ velocities, a phase shift in 1). the emission lines and a large scatter in the radial velocity curves, no reliable white dwarf mass could be derived from the data. UT Date UT UT No. of Phase Phase In addition to this, ? sucessfully modelled the qui- start end spectra start end escent light curve of U Sco with a white dwarf mass of M1 1.37M , a secondary mass of M2 =0.8–2.0M and ∼ an orbital inclination of 80◦. Indirect support that the TNR model is the outburst∼ mechanism in U Sco has also 1999 April 15 14:57 19:09 8 0.31 0.44 been found by the observation of luminous supersoft X-ray 1999 April 16 14:14 19:21 11 0.09 0.26 emission after the 1999 outburst (?). They also constrain 1999 April 17 14:21 19:11 10 0.92 1.07 the white dwarf to be massive from the temperature of the 1999 April 18 14:20 19:16 11 0.72 0.88 optically thick supersoft component. 1999 April 19 14:23 19:30 11 0.54 0.70 In this paper, we present new measurements of the radial velocity semi-amplitude of the primary and secondary stars in U Sco and hence a new determination of the mass of the white dwarf in this system.

approximately 1.0 arcsec and 1.8 arcsec throughout the five nights. 2 OBSERVATIONS U Sco underwent its sixth recorded outburst on 1999 On the nights of 1999 April 15–19 we obtained 51 spectra February 25, reaching a maximum brightness of V = 7.6 (?). of the recurrent nova U Sco with the 3.9m Anglo-Australian The observations recorded in this paper were taken approx- Telescope (AAT) in Siding Springs, Australia. We covered imately 49 days after outburst maximum, as can be seen one complete orbit of U Sco during this time, including an from the lightcurve in Fig. 1, by which time the magni- eclipse – a full journal of observations is given in Table 1. tude had decreased to approximately one magnitude above The exposures were all 1500 s with about 50 s dead-time for its quiescent level. Unfortunately, the single data point in archiving of data. The setup comprised of the RGO Spec- Fig. 1 corresponding to the dates of our observations has no trometer + 250mm camera, the TEK 1024 1024 CCD chip recorded uncertainty. It is therefore impossible to conclude and the 1200V grating, which gave a wavelength× coverage whether we actually observed U Sco during an anomalously 1 of approximately 4620A–5435˚ Aat1.6˚ A(95kms˚ − )reso- high state. What is certain, however, is that the additional lution. We also took spectra of 20 class IV and V spectral shot noise in the continuum made it more difficult than we type templates ranging from F0 – K2, and the flux standard expected to detect absorption lines from the secondary star. LTT 9239 (?). The 1.5 arcsec slit was orientated to cover The total flux in each spectrum is plotted in Fig. 2 as a func- a comparison star 1 arcmin west of U Sco in order to tion of Heliocentric Julian Date (HJD) following equation 1 correct for slit losses.∼ Arc spectra were taken between ev- (see Section 4.1). The eclipse occurs on the third night of ob- ery U Sco exposure to calibrate instrumental flexure. The servation. There is also some evidence for a slight downward nights were all photometric, and the seeing varied between trendinbrightnessoverthefivenights. The recurrent nova U Sco 3

Table 2. Times of mid-eclipse for U Sco according to Schaefer & Ringwald (1995; SR95) and this paper.

Cycle HJD at mid-eclipse O-C Reference (E) (2,440,000+) (secs)

0 7717.5968 0.0139 -1530.6 SR95 1 7718.8412 ± 0.0069 -334.1 SR95 4 7722.5318 ± 0.0139 -425.4 SR95 5 7723.7783 ± 0.0139 952.5 SR95 8 7727.4699 ± 0.0139 947.6 SR95 1168 9154.9111 ± 0.0104 1003.5 SR95 1496 9558.5240 ± 0.0069 293.1 SR95 1497 9559.7497 ± 0.0069 -126.1 SR95 1500 9563.4432 ± 0.0139 33.2 SR95 Figure 2. Light curve of U Sco during our observations. The 2900 11286.2143 ± 0.0050 -141.3 This Paper solid curve is a parabolic ﬁt to the eclipse minimum. ±

4.2 Average Spectrum 3DATAREDUCTION The average spectrum of U Sco is displayed in Fig. 3, and in We debiased the data and corrected for the pixel-to-pixel Table 3 we list fluxes, equivalent widths and velocity widths variations with a tungsten lamp flat-field. The sky was sub- of the most prominent lines measured from the average spec- tracted by fitting second-order polynomials in the spatial trum. direction to the sky regions on either side of the object spec- The spectrum is dominated by single-peaked emission ˚ tra. The data were then optimally extracted (?)togiveraw lines between λλ4870–5080A originating from the recent spectra of U Sco and the comparison star. Arc spectra were outburst. The identification of these nebular lines is compli- then extracted from the same locations on the detector as cated by their large widths, but the blend is likely to have the targets. The wavelength scale for each spectrum was in- contributions from NII, NIII, NV, OIII and OV, indicating terpolated from the wavelength scales of two neighbouring a very high degree of excitation. Both ? and ? attribute the arc spectra. The root-mean-square error in the fourth-order complex around λ5015A˚ toablendofHeIandNIIinthe polynomial fits to the arc lines was 0.025A.˚ 1987 and 1999 outbursts, respectively. ? suggest in the 1979 ∼ outburst the presence of Hβ at λ4861A,˚ and strong OIII ˚ The next stage of the reduction process was to correct emission at λλ4959/5007A. This is supported by compari- for the instrumental response and slit losses in order to ob- son with nebulae around classical novae such as Nova Cygni ˚ tain absolute fluxes. A third-order spline fit to the contin- 1992 (?). There is also evidence of CIV emission at λ4658A, uum of the spectrophotometric standard star was used to in agreement with the 1987 outburst (?). The other strong remove the large-scale variations of instrumental response features in the blend are likely to be due to NIII and NV, in with wavelength. The slit-loss correction was performed by agreement with ?, and optical spectra of Nova GQ Muscae dividing the U Sco spectra by spline fits to the comparison 1983 (?). It is difficult to directly compare our spectra to star spectra, and then multipling the resulting spectra by a the spectra of the 1979 outburst (?) and the 1987 outburst spline fit to a wide-slit comparison star spectrum. (?) because the latter two datasets were taken much closer to the eruption. U Sco also shows strong, broad, double-peaked He II lines at λ4686Aand˚ λ5412A,˚ typical of emission from an accretion disc in a high inclination system (e.g. ?). 4RESULTS The secondary star features cannot clearly be seen in 4.1 Ephemeris Fig. 3, as the spectra have been averaged without being corrected for orbital motion. Consequently, any faint absorption The times of mid-eclipse were determined by fitting a lines will have been smeared out. parabola to the eclipse minimum (the solid curve in Fig. 2). However, when the orbital motion of the secondary A least-squares fit to the 9 eclipse timings found in ? and star is removed, the MgIb triplet (λλ5167,5173,5184A)˚ can our eclipse yields the following ephemeris: clearly be identified (see Section 4.7 and Figure 10).

Tmid eclipse = HJD 2 447 717.6145 + 1.230 5522 E − 0.0044 0.000 0024 (1) ± ± 4.3 Light Curves The continuum light curve for U Sco was computed by sum- The differences between the observed and calculated ming the flux in the wavelength range λλ5080–5390A,˚ which times of mid-eclipse are given in Table 2. We find no evi- is devoid of emission lines. A polynomial fit to the contin- dence for a non-zero value for P˙ , in agreement with ?. uum was then subtracted from the spectra and the emission 4 T. D. Thoroughgood et al.

Figure 3. The average spectrum of U Sco, uncorrected for orbital motion.

Table 3. Fluxes and widths of prominent lines in U Sco, measured from the average spectrum. The wavelength range of the blend is λλ4870–5080A.˚

Line Flux EW FWHM FWZI 14 1 1 10− Akms˚ − km s− × 2 1 ergs cm− s−

HeII λ4686A˚ 1.345 0.007 6.98 0.04 700 50 1600 100 ± ± ± ± HeII λ5412A˚ 0.177 0.005 1.18 0.03 700 100 1500 300 Blend 11.95 ± 0.02 82.9 ± 0.1 ± ± ± ± line light curves were computed by summing the residual are produced in a region external to the orbits of the stellar flux after continuum subtraction. components. The resulting light curves are plotted in Fig. 4 as a function of phase, following our new ephemeris. The contin- 4.4 Trailed spectrum uum shows a symmetrical eclipse, with flickering through- We subtracted polynomial fits to the continua from the spec- out. There appears to be a dip in magnitude around phase tra and then rebinned the spectra onto a constant velocity- 0.5, perhaps indicative of a secondary eclipse, but there are interval scale centred on the rest wavelength of the lines. The too few data points to be conclusive. In addition, as a con- rest wavelength of the nebular lines was taken as 4975A.˚ sequence of U Sco’s long orbital period (1.23 days), the λ The data were then phase binned into 40 bins, 36 of which lightcurves represent data from five nights. Therefore, not were filled. Fig. 5 shows the trailed spectra of the HeII all of the variability can be necessarily attributed to orbital 4686A,˚ HeII 5412A˚ and nebular lines in U Sco. effects. λ λ The HeII lines show two peaks, which vary sinusoidally The eclipses of the HeII lines have a different shape from with phase. This, and the rotational disturbance (where the the continuum. Both lightcurves show a long egress, and blue-shifted peak is eclipsed before the red-shifted peak) is a pre-eclipse increase in brightness. There is no evidence evidence for origin in a high inclination accretion disc. There for significant variability in the lightcurve of the nebular is also some evidence for an emission component moving lines (λλ4870–5080A),˚ supporting the idea that the lines from blue to red between phases 0.6 – 0.9. The recurrent nova U Sco 5

Figure 4. Continuum and emission line lightcurves of U Sco. The open circles represent points where the real data (the closed circles) have been folded over. 6 T. D. Thoroughgood et al.

Figure 5. Trailed spectra of HeII λ4686 A,˚ the nebular lines and HeII λ5412 A.˚ The second panel from the left shows the HeII λ4686 A˚ line computed from the Doppler map. The gaps around phases 0 and 1 in the computed data correspond to eclipse data, which were omitted from the ﬁt; the gaps around phases 0.3, 0.5, 1.3 and 1.5 are due to missing data. The data only cover one cycle, but are folded over for clarity.

4.5 Doppler Tomography white dwarf at intervals of 0.1L1, ranging from 1.0L1 at the red star to 0.3L1. Doppler tomography is an indirect imaging technique which A ring-like emission distribution, characteristic of a Ke- can be used to determine the velocity-space distribution of plerian accretion disc centred on the white dwarf, is clearly line emission in cataclysmic variables. For a detailed review seen in Fig. 6. There is some evidence for an increase in of Doppler tomography, see ?. emission downstream from where the computed gas stream Fig. 6 shows the Doppler map of the HeII λ4686A˚ line in joins the accretion disc, implying the presence of a bright U Sco, computed from the trailed spectra of Fig. 5 but with spot. This kind of behaviour has been seen in other CVs – the eclipse spectra removed. The data for the HeII λ5412A˚ e.g. WZ Sge (?). line were too noisy to produce a Doppler map. The three crosses on the Doppler map represent the centre of mass of the secondary star (upper cross), the centre of mass of 4.6 Radial velocity of the white dwarf the system (middle cross) and the centre of mass of the white dwarf (lower cross). These crosses, the Roche lobe of The continuum-subtracted data were binned onto a constant the secondary star, and the predicted trajectory of the gas velocity interval scale about each of the two helium line rest stream have been plotted using the radial velocities of the wavelengths. In order to measure the velocities, we used the 1 primary and secondary stars, KW =93 10 km s− and double-Gaussian method of ?, since this technique is sensi- 1 ± KR = 170 10 km s− , derived in Section 4.9. The series tive mainly to the motion of the line wings and should there- of circles along± the gas stream mark the distance from the fore reﬂect the motion of the white dwarf with the highest The recurrent nova U Sco 7

Figure 7. Radial velocity curve of HeII λ4686A,˚ measured using 1 a double-Gaussian fit with a separation of 1000 km s− .Points marked by open circles were not included in the radial velocity fit, as they were affected by the rotational disturbance during primary eclipse. The horizontal dashed line represents the systemic velocity.

Figure 6. Doppler map of HeII λ4686A˚ emission in U Sco. reliability. We varied the Gaussian widths between 150–300 1 1 km s− at 50 km s− intervals, as well as varying their sepa- 1 ration a from 200–1500 km s− . We then ﬁtted

V = γ K sin[2π(φ φ0)] (2) − − to each set of measurements, omitting the 9 points around primary eclipse which were affected by the rotational disturbance. An example of a radial velocity curve obtained for 1 the HeII λ4686A˚ line for a Gaussian width of 300 km s− 1 and separation 1000 km s− is shown in Fig. 7. The data for the HeII λ5412A˚ line were too noisy to determine accurate radial velocities. The radial velocity curve has a negligible phase offset, an indication that the helium line is a reliable representa- tion of the motion of the white dwarf. The results of the radial velocity analysis are displayed in the form of a diagnostic diagram in Fig. 8. By plotting K, its associated fractional error σK /K, γ and φ0 as functions of the Gaus- sian separation, it is possible to select the value of K that most closely represents the actual KW (?). If the emission were disc dominated, one would expect the solution for K to asymptotically reach KW when the Gaussian separation becomes sufficiently large, and furthermore, one would expect φ0 to fall to 0. This is seen to occur at a separation 1 1 of 1200 km s− , corresponding to KW 93 km s− .There ∼ ∼ is, however, no sudden increase in σK /K, prompting us to employ a different approach. Figure 8. The diagnostic diagram for U Sco based on the double- ? suggests that the use of a diagnostic diagram to eval- Gaussian radial velocity fits to HeII λ4686A.˚ uate KW does not account for systematic distortion of the radial velocity curve. We therefore attempted to make use of the light centres method, as described by ?.Intheco- rotating co-ordinate system, the white dwarf has velocity (0, KW ), and symmetric emission, say from a disc, would − be centred at that point. By plotting Kx = K sin φ0 versus − Ky = K cos φ0 for the different radial velocity fits (Fig. 9), − one finds that the points move closer to the Ky axis with 8 T. D. Thoroughgood et al.

Figure 9. Light centres diagram for HeII λ4686AinUSco.˚ increasing Gaussian separation. A simple distortion which only affects low velocities, such as a bright spot, would result in this pattern, equivalent to a decrease in distortion as one measures emission closer to the velocity of the primary star. By extrapolating the last point on the light centre diagram to the Ky axis, we measure the radial velocity semi- 1 amplitude of the white dwarf KW =93 10 km s− .The ± Figure 10. Normalized spectra of ten template stars. The offset error on KW was estimated from the uncertainty in cross- between each is 0.035. The U Sco spectrum is a normalized aver- ing the Ky axis, given the uncertainties associated with the points on the light centres diagram. Note the small scale on age of 43 of the 51 spectra observed; 8 spectra were omitted due to cosmic rays interfering with secondary features. The template the x–axis of the light centres diagram. 1 spectra have been broadened by 16 km s− to account for orbital 1 smearing of the U Sco spectra during exposure and by 88 km s− to account for the rotational broadening of the lines in U Sco. 4.7 Radial velocity of the secondary star The secondary star in U Sco is observable through weak absorption lines, although many features have been drowned of the templates yielding a time series of cross-correlation out by the nebular lines of the outburst. We compared re- functions (CCFs) for each template star. gions of the spectra rich in absorption lines with several tem- To produce the skew map (Fig. 11), these CCFs were plate dwarfs of spectral types F0–K2, the spectra of which back-projected in the same way as time-resolved spectra in are plotted in Fig. 10. The absorption features are too weak standard Doppler tomography (?). If there is a detectable for the normal technique of cross-correlation to be successful secondary star, we would expect a peak at (0,KR)inthe in finding the value of KR, but it is possible to exploit these skew map. This can be repeated for each of the templates. features to obtain an estimate of KR using the technique of When we first back-projected the CCFs, the peak in skew mapping. This technique is descibed by ?. each skew map was seen to be displaced to the blue of the 1 The first step was to shift the spectral type template Kx = 0 axis by around 30 km s− . The reason was that stars to correct for their radial velocities. We then normal- we assumed that the centre of mass of the system was at ized each spectrum by dividing by a spline fit to the contin- rest. The systemic velocity of U Sco derived from the radial 1 uum and then subtracting 1 to set the continuum to zero. velocity curve fits in Section 4.6 is γ =47 10 km s− . ± This ensures that line strength is preserved along the spec- Applying this γ velocity shifts the peak to the red, towards 2 2 trum. The U Sco spectra were also normalized in the same the Kx = 0 axis. As Kx Ky , then the value of KR is way. The template spectra were artificially broadened by 16 given by the equation 1 km s− to account for orbital smearing of the U Sco spectra 2 2 1/2 KR =(K + K ) Ky, through the 1500 s exposures. The rotational velocity of the x y ≈ secondary star was found by the equation so KR changes little whilst varying γ.

3 The skew maps produced using each of the tem- 1 2 v sin i plate stars with γ =0kms− show well-defined peaks q(1 + q) =9.6 (3) 1 KR at (Kx,Ky) ( 30, 160) km s− . However, applying γ = ! 1 ∼ − 47 km s− , the peaks in the skew maps shift to (Kx,Ky) 1 ∼ (?) using estimated values of q and KR in the first instance, (15, 180) km s− . We suspect that the true γ value of U Sco then iterating to find the best fit values given in Section 4.9. falls between these two limits. The skew map shown in The templates were then broadened by this value of v sin i Fig. 11 is for the K2V spectral type template with γ = 1 1 =88kms− . Regions of the spectrum devoid of emission 47 km s− , and is arguably the best fitting template for the lines (λλ5085 5395A)˚ were then cross-correlated with each secondary star. The skew map shows a clear peak around − The recurrent nova U Sco 9

1 (Kx,Ky) (10, 165) km s− . To bring the skew map peak ∼ to lie on Kx =0,theγ value must be modified to 30 1 ∼ km s− , which still falls within 2σ of the γ derived from the 1 emission lines. The resulting peak falls on Ky = 170 km s− , which we adopt as the radial velocity semi-amplitude for 1 the secondary star: KR = 170 10 km s− . The uncertainty ± in KR has been determined from the scatter in KR due to four sources of error: varying the γ velocity; using different spectral type templates; producing skew maps from random subsets of the data; the accuracy in measuring the peak in the skew map. The bottom panel of Fig. 11 shows a sine wave in the trailed CCFs, demonstrating that the peak in the skew map is not due to noise in the CCFs. It can be seen that the peaks in the CCFs are most prominent around primary eclipse (φ 0.7–1.2). There are two possible explanations for this. First,∼ by considering the geometry of the secondary eclipse in U Sco, we estimate that a maximum of 30 per cent of the visible surface of U Sco will be obscured by the large accretion disc (see Section 4.9) between phases 0.35–0.65. We would therefore expect the peaks in the CCFs to weaken considerably at these phases, which is exactly as observed in Figure 11. This explanation is further supported by the tentative evidence for a secondary eclipse presented in the continuum light curve (Figure 4) and it does not affect the values for the masses we have derived in Section 4.9. Second, it is possible that the absorption features on the inner hemi- sphere of the secondary star are weakened by irradiation due to the recent outburst, which would again explain the loss of the peaks in the CCFs around phase 0.5. If the latter explanation were true, it is possible that we have overestimated the value of KR, which would in turn lead us to overestimate M1 (see Figure 12). The only way we can reliably account for any systematic effects due to irradiation would be to obtain higher signal-to-noise observations during quiescence and so measure v sin i during primary eclipse.

4.8 Rotational velocity and spectral type of Figure 11. The top panel shows the skew map of U Sco for the the secondary star K2V spectral type template. The bottom panel shows the trailed Mass estimates of CVs using emission line studies suffer from CCFs for the same template, clearly demonstrating that the peak in the skew map represents K and is not an artefact of noise in systematic errors, and have been thoroughly discussed by a R the CCFs. The dashed line shows our adopted parameters for the number of authors (e.g. ?). More reliable mass estimates can 1 1 secondary star orbit: KR = 170 km s− , γ =47kms− and zero be obtained by using KR in conjunction with the rotational phase shift. The data have been folded over for clarity. velocity of the secondary star, v sin i. We attempted to determine v sin i using the procedure outlined in ?, but the data were too noisy. confirm a secondary spectral type using our data, although Previous estimates of the secondary spectral type have the MgIb complex is clearly present. ranged from F5V to K2III. ? suggests G0 5III-V, corrob- ± orated by ? with a GIII subgiant. Recent estimates have agreed on the subgiant nature of the secondary. ? estimated 4.9 System Parameters the spectral type as G3-6 from the colours at minimum light, whereas ? measured the observed ratio of calcium lines to The radial velocity curves show little or no phase shift, giv- Hδ and found F8 2. Based on the detection of the MgIb ing us confidence that our measurement of KW reflects the ± absorption in the 1979 outburst spectrum, ? find the sec- motion of the white dwarf. Hence, together with KR,our ondary to be consistent with a low-mass subgiant secondary newly derived period and a measurement of the eclipse full of spectral type K2. This is supported by ?, who estimate width at half-depth (∆φ1/2), we can proceed to calculate ac- the secondary to be a K2 subgiant based on the indices of curate masses free of many of the assumptions which com- the MgIb absorption band and the FeI + CaI absorption monly plague CV mass determinations. Our white dwarf 1 feature in the late-decline spectrum of the 1999 outburst. radial velocity semi-amplitude, KW =93 10 km s− com- ± Unfortunately, as can be seen in Fig. 10, it is impossible to pares favourably with the previous measurement of KW = 10 T. D. Thoroughgood et al.

1 95 50 km s− by ? after the 1979 outburst. ? derived the Table 4. System parameters for U Sco ± 1 1 values KW =87 32 km s− and KR =56 27 km s− , but concluded that these± results were unreliable± due to inconsistent velocities, a phase shift in the emission lines and a γ Parameter Measured Value Monte Carlo Value large scatter in the radial velocity curves.

In order to determine ∆φ1/2, we estimated the levels of ﬂux outside the eclipse (the principle source of the error) and at eclipse minimum, and then measured the full width Porb (d) 1.2305522 1 of eclipse half way between these points. The eclipse full KW (km s− )9310 95 9 1 ± ± width at half-depth for U Sco was measured to be ∆φ1/2 = KR (km s− ) 170 10 169 10 ± ± 0.104 0.01, in good agreement with ∆φ1/2 =0.106 0.01 ∆φ 0.104 0.010 0.098 0.007 ± ± 1/2 ± ± cited by ?. q 0.55 0.07 ± We have opted for a Monte Carlo approach similar to i◦ 82.7 2.9 ± that of ? to calculate the system parameters and their errors. M1/M 1.55 0.24 ± For a given set of KW , KR,∆φ1/2 and P , other system M2/M 0.88 0.17 ± parameters are calculated as follows. R2/R 2.1 0.2 ± The mass ratio, q, can be determined from the ratio of a/R 6.5 0.4 ± the radial velocities ∆φ 0.12 0.01 ± M K RD/R1 0.87 0.11 q = 1 = W . (4) ± M2 KR

R2/a can be estimated because we know that the secondary star ﬁlls its Roche lobe (as there is an accretion disc present and hence mass transfer). R2 is the equatorial radius of the secondary star and a is the binary separation. We used Eggleton’s formula (?) which gives the volume-equivalent radius of the Roche lobe to better than 1 per cent, which is dius of the secondary star, and the separation of the compo- close to the equatorial radius of the secondary star as seen nents, as outlined above, omitting (KW ,KR,∆φ1/2) triplets during eclipse, which are inconsistent with sin i 1. Each accepted M1,M2 pair is then plotted as a point in≤ Fig. 12, and the masses R 0.49q2/3 2 = . (5) and their errors are computed from the mean and standard a 0.6q2/3 +ln(1+q1/3) deviation of the distribution of spots. The solid curves in By considering the geometry of a point eclipse by a spherical Fig. 12 satisfy the white dwarf radial velocity constraint, 1 body (e.g. ), the radius of the secondary can be shown to KW =93 10 km s− and the secondary star radial ve- ? ± 1 locity constraint, KR = 170 10 km s− . We ﬁnd that be ± M1 =1.55 0.24M and M2 =0.88 0.17M .Thein- 2 ± ± R2 2 2 2 clination of the system is calculated to be i =82.7◦ 2.9◦, = sin π∆φ1/2 +cos π∆φ1/2 cos i. (6) ± a consistent with the nature of the deep eclipse seen in the lightcurves and the presence of double-peaked helium emis- Using the value of R2/a obtained from equation 5, combined sion. with equation 6, the inclination of the system can be found. We computed the radius of the accretion disc in U Sco Kepler’s Third Law gives using the geometric method outlined in ?. The phase half- K3 P M sin3 i width of eclipse at maximum intensity was found to be R orb = 1 (7) 2πG 2 ∆φ =0.12 0.01 from Figure 4. Combining ∆φ with q (1 + q) ± and i derived above produces an accretion disc radius of which, with the values of q and i calculated using equa- RD =0.87 0.11R1,whereR1 isthevolumeradiusof tions 4, 5 & 6, gives the mass of the primary star. The mass ± the primary’s Roche lobe. Our values for ∆φ and RD are of the secondary star can then be obtained using equation 4. consistent with those found by ?:∆φ =0.129 0.008 and The distance of each component to the centre of mass of the ± RD 0.92R1. ≥ system (a1,a2), is given by The empirical relation obtained by ? between mass and K P radius for the secondary stars in CVs is given by, a = (W,R) (8) (1,2) 2π sin i The separation of the two components, a,isa1 +a2, allowing R M the radius of the secondary star, , to be calculated from =(0.93 0.09) +(0.06 0.03). (9) R2 R ± M ± equation 5. ! The Monte Carlo simulation takes 10 000 values of KW , KR,and∆φ1/2 (the error on the period is deemed to be This predicts that if the secondary star is on the main- negligible in comparison to the errors on KW , KR,and sequence, it should have a radius of 0.88R .Thevaluewe

∆φ ), treating each as being normally distributed about ﬁnd is 2.1 0.2R , clearly indicating that the white dwarf 1/2 ± their measured values with standard deviations equal to the in U Sco has an evolved companion. errors on the measurements. We then calculate the masses The values of all the system parameters of U Sco derived of the components, the inclination of the system, the ra- in this section are listed in Table 4. The recurrent nova U Sco 11

Figure 12. Constraints on the masses of the stars in U Sco. Each dot represents an (M1,M2) pair. The dashed lines are lines of constant inclination (i =80 , i =85 , i =90 ). The solid curves satisfy the constraints on K =93 10 km s 1 and K = 170 10 km s 1. ◦ ◦ ◦ W ± − R ± −

5 DISCUSSION 5.2 U Sco as a Type Ia SN Progenitor

5.1 TNR Model Type Ia supernovae (SNe Ia) are widely believed to be thermonuclear explosions of mass-accreting white dwarfs (see ? for a review). The favoured model for progenitor binary systems is the Chandrasekhar mass model, in which a mass- The outburst events in RNe could be the result of the TNR accreting carbon-oxygen white dwarf grows in mass up to model, as seen in classical novae, or the disc instability model the Chandrasekar limit and then explodes as a SN Ia. For of dwarf novae. It is likely that given the heterogeneous na- the evolution of accreting WDs towards the Chandrasekhar ture of RNe, the mechanism depends on the individual sys- mass, two scenarios have been proposed. The first is a dou- tem (?). In the case of U Sco, the TNR model was sug- ble degenerate scenario, where two white dwarfs merge to gested in the light of severe problems with the disc instabil- cross the Chandrasekhar limit. A candidate for this has been ity model (?). The motivation behind measuring the mass of identified in KPD 1930+2752 (?). The second is a single de- the white dwarf in U Sco was to give positive confirmation generate scenario, where matter is accreted via mass transfer that outbursts are the result of a TNR, which predicts that from a stellar companion. A new evolutionary path for single the higher the mass of the white dwarf, the more frequent degenerate progenitor systems is discussed by ?, which de- the outbursts. For eruptions to recur on the timescales seen scibes how the secondary (a slightly evolved main-sequence in U Sco ( 8 years), the mass of the white dwarf must be star) becomes helium rich. Their progenitor model predicts ∼ very close to the Chandrasekhar mass of 1.378M (?; ?; ?). helium enriched matter accretion onto a white dwarf. Ob-

Our observations allow us to calculate the mass of the white jects which display these characteristics in the form of strong dwarf in U Sco to be M1 =1.55 0.24M . Despite the large HeIIλ4686A˚ lines are luminous super-soft X-ray sources and error on the value, we can conclude± that U Sco contains certain recurrent novae, such as U Sco and the others in the a high mass white dwarf, although additional work, such as U Sco subclass (V394 CrA and LMC-RN). The observations an accurate v sin i determination during quiescence, must be in this paper, in conﬁrming the helium rich accreted mat- done to further constrain this. ter, and constraining the white dwarf mass to be near the 12 T. D. Thoroughgood et al.

Chandrasekhar mass, make U Sco the best candidate for this evolutionary path to a SN Ia. The time to supernova can be estimated by dividing the amount of mass required to reach the Chandrasekhar mass by the average mass accretion rate (M˙ av). Our results suggest a minimum white dwarf mass of 1.31M ,which ∼ requires it to accrete approximately 0.07M to become a

SN Ia. In their model, ? ﬁnd that the white dwarf in U Sco 7 grows in mass at an average rate of M˙ av 1.0 10− M 1 ∼ × y− . Using this value, we therefore predict U Sco to become a supernova within 700 000 years. ∼

6CONCLUSIONS (i) We have shown that U Sco contains a high mass white dwarf (M1 =1.55 0.24M ), conﬁrming that the out-

burst mechanism is± the TNR model. (ii) The presence of an accretion disc has been conﬁrmed for the ﬁrst time by clear evidence of rotational disturbance in the HeII emission lines during eclipse, as well as their double-peaked nature. (iii) The secondary star has a radius of 2.1 0.2R , consis-

tent with the idea that it is evolved. ± (iv) The mass of the white dwarf in U Sco is M1 =1.55 ± 0.24M , implying that it is the best SN Ia candidate

known and is expected to explode in 700 000 years. ∼

Acknowledgements

We would like to thank Katsura Matsumoto, Taichi Kato and Izumi Hachisu for their light curve of U Sco during the 1999 outburst, and Chris Watson for useful comments. TDT and SPL are supported by PPARC studentships. The authors acknowledge the data analysis facilities at Sheﬃeld provided by the Starlink Project which is run by CCLRC on behalf of PPARC. The Anglo-Australian Telescope is oper- ated at Siding Springs by the AAO.